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Old 01-24-2020, 04:54 PM
jerrytuttle jerrytuttle is offline
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Default Principal Component Analysis

I am having trouble understanding Principal Component Analysis, which I understand is now part of MAS !!. Would someone kindly share a simple numerical example in Excel or R so I can follow the calculation, and also explain what one then does with the numerical result?

Thank you,
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Old 01-24-2020, 04:58 PM
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AbedNadir AbedNadir is offline
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Old 01-27-2020, 08:54 PM
Colymbosathon ecplecticos's Avatar
Colymbosathon ecplecticos Colymbosathon ecplecticos is offline
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It's probably easier to think about it geometrically.

PCA is a dimension reduction technique. Suppose that you have a data set with three variables.

Your data looks like (X+noise1, 3X+noise2, -X+noise3) where X is some random variable and noisei (i=1,2,3) is, well, noise (and small compared to X on average.

The data set looks like a thickened blob lying along the subspace spanned by (1, 3, -1).

PCA asks the question: if I had to approximate this dataset with a single direction (one dimensional subspace), which direction should I use. The answer has several interpretations: which direction captures the most variation I the dataset?

Once that direction is known, we project the dataset onto it, compute the orthogonal complement and repeat. This yields a sequence of vectors which we use (in order) to form a nested sequence of vector spaces (of dimensions, 1, 2, 3, ) that are in some sense best approximations to our data.

That should get you started.
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